Journal ofTesting and Evaluation

A. Hijazi1 and C. J. Kahler2

DOI: 10.1520/JTE20150437

Contribution of the ImagingSystem Components in theOverall Error of theTwo-Dimensional Digital ImageCorrelation Technique

VOL. 45 / NO. 2 / MARCH 2017

A. Hijazi1 and C. J. Kahler2

Contribution of the Imaging SystemComponents in the Overall Error of theTwo-Dimensional Digital ImageCorrelation Technique

Reference

Hijazi, A. and Kahler, C. J., “Contribution of the Imaging System Components in the Overall Error of the

Two-Dimensional Digital Image Correlation Technique,” Journal of Testing and Evaluation, Vol. 45, No. 2,

2017, pp. 1–16, doi:10.1520/JTE20150437. ISSN 0090-3973

ABSTRACT

Digital image correlation (DIC) is one of the most widely used non-invasive methods for

measuring full-field surface strains in a wide variety of applications. The DIC method has

been used by numerous researchers for measuring strains during the plastic range of

deformation where the strains are relatively large. The estimation of the amount of

background strain error in the measurements is of prime importance for determining the

applicability of this method for measuring small strains (such as the elastic strains in

metals, ceramics, bone samples, etc.). In this study, the strain errors in 2D-DIC

measurements associated with different types of imaging systems were investigated.

In-plane rigid-body-translation, experiments were used to estimate the overall amount of

error in DIC displacement and strain measurements. Different types of cameras having

different types of sensors and different spatial resolutions were used in the study. Also,

for the same type of camera, different types of lenses were used. Results show that the

DIC measurement accuracy depends on the magnitude of image displacement and that

different error estimation parameters can be used for quantifying the accuracy of the

measurements. Also, the effect of the lens on measurement accuracy is more pronounced

than that of the camera. Furthermore, imaging conditions such as image sharpness and

camera gain also affect the accuracy. Further still, the measurement accuracy was found

to be influenced by the direction of translation. The results indicate that measurement

error can be reduced by orienting the camera such that the major displacement direction

is parallel to the width direction of the image. The experimental approach used in this

study can be used for quantitatively assessing the quality of the different types of

Manuscript received October 14, 2015;

accepted for publication January 25,

2016; published online February 29,

2016.

1 Department of Mechanical Engineering,

The Hashemite Univ., Zarqa, 13115,

Jordan (Corresponding author),

e-mail: hijazi@hu.edu.jo

2 Institute of Fluid Mechanics and

Aerodynamics, Universitat der

Bundeswehr Munchen,

85577 Neubiberg, Germany.

Copyright VC 2016 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. 1

Journal of Testing and Evaluation

doi:10.1520/JTE20150437 / Vol. 45 / No. 2 / March 2017 / available online at www.astm.org

cameras and lenses and to determine their suitability for use in experimental techniques that depend on image analysis such

as DIC and particle image velocimetry (PIV).

Keywords

digital image correlation, error analysis, strain error, imaging system, camera, CCD, CMOS, lens distortion

Introduction

Nowadays, digital image correlation (DIC), sometimes referred

to as the digital speckle correlation method (DSCM), has

become one of the most widely used full-field optical methods

for motion and deformation measurements. The DIC method

was first introduced by Sutton et al. [1] in the early 1980s,

and during the past three decades it underwent continuous

modifications and significant improvements [2,3]. In its simpler

version, DIC is used for two-dimensional in-plane measure-

ments (2D-DIC) using a single camera. Also, photogrammetric

three-dimensional measurements (3D-DIC) [4] can be made

using two cameras in stereo configuration. Besides the good

measurement accuracy of the DIC method, it also offers other

attractive features which include a relatively simple experimen-

tal setup, simple or no specimen preparation, and low require-

ments for the measurement environment. All of that has made

the DIC method extremely popular among the experimental

mechanics community, and both 2D-DIC and 3D-DIC are

being increasingly used in a very wide range of applications

ranging from material science to mechanical, manufacturing,

biomedical, and structural engineering [5,6].

The basic idea of DIC is to compare two digital images,

acquired at different states (e.g., one before deformation and the

other one after), of a surface having a random speckle pattern

to determine the magnitude of displacement (or deformation)

between the two images. The comparison is done by dividing

the reference image into subsets of several pixels, then mathe-

matically matching those subsets with the other image (based

on intensity levels). By doing such, the new location of each

subset in the second image can be determined. From that, the

full-field deformation map can be obtained and the strain map

can then be easily determined.

Digital particle image velocimetry (DPIV, or usually just

referred to as PIV) [7–9] is a technique that is somehow similar

to DIC; however, it is used in experimental fluid mechanics for

obtaining the fluid velocity map within a region of interest.

Small seeding particles are introduced into the flow and the

kinematics of the fluid flow is estimated by tracking the motion

of these particles. The particles are chosen to have a density

such that they will be near naturally buoyant in the fluid in

order to faithfully follow the flow. The region of interest is illu-

minated using a thin planar light sheet (usually a laser is used

for illumination) such that the seeding particles within this light

sheet will be visible due to the light scattered off their surfaces.

The motion of the particles within the light sheet is captured

using a digital camera where typically two exposures with a

small inter-frame separation are recorded by the camera. By

comparing any two consecutive digital images (using techniques

quite similar to those used in DIC), the magnitude and direction

of motion of the seeding particles can be determined. Finally,

the magnitude of motion is divided by the inter-frame time sep-

aration between the two images such that the 2D velocity field

of the flow is obtained. Though DIC and PIV are used in totally

different applications, however, the two techniques are quite

similar in terms of the analyses performed on the captured

images. The first step in both techniques is basically the same

where the motion of each of the image subsets is determined,

though different correlation algorithms are typically used [3,10].

The difference between the two techniques comes in the second

step. In DIC, the motion map is used to calculate the strains,

whereas in PIV the motion map is divided by the inter-frame

time separation to calculate the velocity. Some of the commer-

cial software packages available nowadays are capable of

performing both DIC and PIV analyses.

In principle, 2D-DIC can be used for deformation measure-

ments under three conditions: the specimen has a planar sur-

face, it undergoes in-plane deformations, and the camera’s

optical axis is perpendicular to the specimen surface. If any of

these three conditions is not reasonably satisfied, the accuracy

of the measurements will be compromised. The measurement

accuracy of 2D-DIC depends on several factors, which include:

(a) the speckle pattern, (b) quality and perfection of the imaging

system (distortions, noise, resolution, etc.), and (c) the selection

of the correlation algorithm and parameters (subset and step

size, correlation and shape functions, sub-pixel algorithm, etc.)

[3,5]. Numerous studies have investigated the different sources

of error and tried to estimate the resulting errors and to suggest

remedies in some cases. Listings of the different studies can be

found in Refs. [3,5,11]. Similarly, there have been several studies

that addressed the accuracy of PIV measurements [10,12–14].

The majority of the studies aimed at investigating the accuracy

of the DIC or PIV measurements (especially for PIV) use simu-

lated digital images with artificial deformation patterns in order

to investigate the accuracy of the different correlation algo-

rithms and the effects of the different correlation parameters.

Journal of Testing and Evaluation2

In one of the key papers addressing the applications of DIC

in experimental mechanics, Chu et al. [15] used in-plane rigid-

body-translations to demonstrate the viability of the DIC

method for actual measurements. When a body undergoes a

rigid-body-translation, the measured strains should theoreti-

cally be zero. Thus, any obtained strain readings will actually

reflect an error in the measurement and the magnitude of

the obtained strains is simply the magnitude of error. In a

rigid-body-translation experiment, the camera is directed per-

pendicularly to a surface having a random black and while

speckle pattern, and an image is captured while the surface is at

its initial position, then the surface is rigidly translated in-plane

by a small amount and another image is captured. This simple

experiment remains to be one of the most widely used experi-

ments for estimating the magnitude of background strain error

expected in DIC strain measurements. Several other researchers

have also used in-plane rigid-body-translation experiments to

estimate the expected background error in DIC measurements

under several experimental conditions. Haddadi et al. [16] did

an experimental investigation in which they used rigid-body-

translations to investigate different sources of error in 2D-DIC

measurements and to estimate these errors. In that study, they

estimated the strain errors associated with the magnitude of

in-plane translation, subset and step sizes, in-plane rotation,

speckle pattern, out-of-plane displacement, lightening, and test-

ing environment. Sutton et al. [17] studied the effects of out-of-

plane displacements and rotations (that may occur during the

loading) both theoretically and experimentally using rigid-

body-translations. Their results show that out-of-plane transla-

tion could lead to significant error in 2D-DIC strain measure-

ments, especially for short camera-to-object stand-off distance.

They also showed that the use of telecentric lenses minimizes

the error to a manageable level. Hijazi et al. [18] also used rigid-

body-translations as well as theoretical analysis to study the

influence of camera non-perpendicularity on the measurement

accuracy of 2D-DIC. Their results showed that small amounts

of misalignments could result in relatively large errors in strain

measurements, especially if the camera-to-object stand-off dis-

tance is short. They also showed that the rigid-body-translation

experiments can be used for verifying the perpendicularity of

the camera with respect to the surface being observed.

Researchers have also studied the influence of the lens dis-

tortions on 2D-DIC measurement accuracy for both micro-

scopic and macroscopic levels [19–22]. In fact, the effect of the

lens is more obvious for 2D-DIC than it is for 3D-DIC. This

is simply due to the fact that 3D-DIC measurements involve a

rigorous pre-measurement calibration procedure, which can

correct lens distortions to a reasonable extent. However,

2D-DIC, on the other hand, is generally used without any pre-

measurement calibration where this is regarded as one of the

attractive features for this method. Pan et al. [21] investigated

the 2D-DIC strain measurement error due to lens distortion

both theoretically and experimentally. They proposed a simple

first order lens distortion correction method to correct for radial

distortion and they applied it to images recorded using a tele-

centric lens during in-plane rigid-body-translation experiments.

Similarly, Lava et al. [22] also studied the impact of lens distor-

tions on 2D-DIC strain measurements accuracy using in-plane

rigid-body-translation experiments. They developed a correc-

tion method that corrects for radial and tangential lens distor-

tions and they applied their calibration procedure for three

lenses having different focal lengths (12, 23, and 50mm). Rue

et al. [23] studied the influence of the imaging system (camera

and lens) resolution on 2D-DIC measurements. They used syn-

thetic and experimental images with different resolutions and

concluded that a careful choice for the camera/lens combination

should be made for DIC measurements where one of the two

components can be resolution limiting. Barranger et al. [24]

investigated the effect of the camera dynamic range (i.e., gray

scale bit depth) on DIC measurement accuracy using in-plane

rigid-body-translation experiments. They compared three dif-

ferent cameras with 8-bit, 10-bit, and 12-bit dynamic range and

they observed that the 8-bit camera gives higher accuracy than

the ones with higher dynamic range. Tiwari et al. [25] per-

formed an assessment for the applicability of using high-speed

cameras (frame rates higher than 1000 fps) for DIC measure-

ments. They compared two types of high-speed cameras, an

ultra-high-speed multi-channel intensified CCD camera and a

high-speed CMOS camera. Their results showed that the CMOS

camera gives slightly better accuracy for DIC measurements

and that both cameras can yield reasonably accurate strain mea-

surement after applying a calibration procedure to remove

image distortions.

From the above literature survey it is evident that there is a

lack of studies that discretely investigate and quantify the effect

of the imaging system components (both cameras and lenses)

on 2D-DIC measurement accuracy. Comparing different types/

classes of cameras and lenses that are widely used in DIC and

identifying the contributions of the cameras and lenses in the

measurements error is of a particular interest for many DIC

users. In the work presented in this study, the strain errors

in 2D-DIC measurements associated with different types of

imaging systems were quantified and compared. A rigorous

experimental procedure that uses in-plane rigid-body-

translation experiments was used to determine the overall

amount of error in DIC displacement and strain measurements

in order to compare the different cases that were investigated

here. Different types of cameras having different types of sen-

sors were used in the study. Also, for the same type of camera,

different types of lenses were used. In addition, different mea-

surement error estimation parameters that are typically used for

DIC accuracy measurement were compared. Furthermore, the

effect of the direction of the in-plane translation on measure-

ment error was also investigated.

HIJAZI AND KAHLER ON IMAGING SYSTEM EFFECT ON 2D-DIC ERROR 3

Digital Imaging Devices

An image capturing device consists of an imaging optic (i.e.,

lens) which collects the light emanating from a target and

forms an image of that target on a light sensitive medium

(electronic image sensor, photographic film, etc.). An elec-

tronic image sensor consists of a matrix of capacitor-like

storage elements, known as pixels, formed on an oxide cov-

ered silicon substrate. This type of sensor, which is known as

the Metal Oxide Semiconductor (MOS) sensor, relies on the

photoelectric property of silicon to convert the incident light

to electrical charge. As an optical image is projected on the

imaging sensor, which is usually referred to as the focal

plane array (FPA), the photons reaching each pixel generate

an electrical charge, usually electrons, the magnitude of

which is proportional to the local intensity of light on that

pixel. After the sensor has been exposed to light for a period

of time (the integration or exposure time), a pattern of

charges is collected in the pixels (i.e., a frame is captured).

The pattern of charges is then readout to a storage device,

freeing the sensor to capture another image. The two most

widely recognized types of MOS sensors are the complemen-

tary metal oxide semiconductor (CMOS) and the charge-

coupled device (CCD). Both the CMOS and CCD sensors

were invented around the same time; however, due to the

more complicated design of CMOS sensors, the CCD tech-

nology developed much faster and CCD sensors became

more dominant. The technological advances during the last

two decades made the manufacturing of CMOS sensors more

economical and thus they are increasingly being used as an

alternative to CCD sensors in many scientific, industrial, and

consumer cameras. The basic difference between CCD and

CMOS sensors is in the way an image (i.e., the pattern of

charges collected in the pixels) is transferred out of the sen-

sor after it has been captured [26]. There are three common

types of CCD sensors which are the “full frame,” the “frame

transfer,” and the “interline” CCDs [27]. The main difference

between these three types is in the layout of the sensor where

each of the three different designs has its advantages and dis-

advantages. A thorough review of the different types of elec-

tronic imaging sensors can be found in Ref. [26] and a

comparison of the performance of different types of imaging

sensors can be found in Ref. [28].

Unlike compact digital cameras used in regular photogra-

phy, which have an electronic sensor and a lens that are inte-

grated into a single unit, imaging systems used in scientific

applications usually come as two separate units: the camera

body and the lens (similar to professional photography cam-

eras). The cost of cameras used in scientific applications vary

significantly according to the type of sensor, its resolution, sig-

nal to noise level, readout speed, frame rate, etc. The same also

applies to lenses according to the quality of the optics and the

amount of optical distortions. Consequently, the cost of imaging

systems used in scientific applications could vary from less than

a thousand dollars to more than $100,000 for some of the high

speed systems.

Experimental Procedures

In this study, in-plane rigid-body-translation experiments were

used to investigate the strain errors in 2D-DIC measurements

associated with different types of imaging systems. Different

classes of cameras having different types of sensors, resolutions,

and dynamic range (bit depth) were used in the study. Also, for

the same type of camera, different types of lenses were used in

order to investigate the effect of the lens on strain error. The

different cameras and lenses that were used in this investigation

along with the main specifications for each are listed in Tables 1

and 2, respectively.

As can be seen from Table 1, four different cameras were

used in this investigation. The SensiCam camera is one of the

high end scientific cameras; it features a cooled FPA which pro-

vides high stability and quantum efficiency. Also, this camera is

capable of operating in a special mode known as “dual-frame

mode,” where it can capture a pair of images with very short

inter-frame time [26], and thus it is commonly used in PIV

applications. The Genie camera is one of the moderate cost

CCD industrial cameras, whereas the Photon Focus camera has

a CMOS sensor with higher dynamic range, and thus its price is

higher. The Canon camera is one of the typical high resolution

SLR digital cameras used in professional photography. Though

it will be elaborated later in the results and discussion section, it

is also worth mentioning here that the Canon color-SLR digital

camera is in fact not comparable to the other cameras that were

used here, and even it was not compared on one-to-one bases in

terms of the lens (as can be seen in Table 3). However, the

TABLE 1 The main specifications of the different cameras used in the experiments.

Camera PCO / SensiCam QE DALSA / Genie-M1410 Photon Focus / MV1-D1312-80 Canon EOS 450D

Sensor Monochrome 2/3 in. interline CCD Monochrome 2/3 in. interline CCD Monochrome 1 in. CMOS Color 11=4 in. CMOS

Resolution 1376� 1040 1360� 1024 1312� 1082 4272� 2848

Dynamic range 12-bit 8-bit 12-bit 24-bit (color)

Frame rate 10 fps 22 fps 55 fps 3.5 fps

Lens mount C-mount C-mount C-mount EF-mount

Journal of Testing and Evaluation4

Canon camera was included in this investigation simply because

similar cameras are used by some DIC users, in addition to the

fact that some DIC software companies commercialize similar

cameras as an alternative for applications where DIC measure-

ments need to be done in the field.

Table 2 lists the four different types of lenses that were used

in this investigation. The Zeiss lens is a high quality lens with

high aperture (i.e., a fast lens) and very low optical and chro-

matic aberrations. The Pentax lens is a small size, good quality

lens designed for machine vision applications and it comes at a

moderate price. The Nikon zoom lens is an old model lens that

was designed for use with old-style film SLR cameras. The

Canon zoom lens is the default lens that is supplied with the

Canon EOS camera, and it can be operated in the automatic or

manual focus modes.

In order to investigate the influence of the different types of

cameras and lenses on DIC measurements accuracy, different

combinations of the cameras and lenses were used in the experi-

ments as listed in Table 3. As can be seen in the table, six differ-

ent camera/lens combinations were used in the experiments.

The SensiCam/Zeiss, Genie/Zeiss, and Photon Focus/Zeiss com-

binations were used to study the effect of the camera, whereas

the Genie/Zeiss, Genie/Pentax, and Genie/Nikon were used to

study the effect of the lens. An F-mount to C-mount adaptor

was used to fit the Zeiss and Nikon lenses on the cameras. The

Canon camera, on the other hand, was only used with its own

lens mainly because the other lenses do not fit this camera, as

it has a large size FPA. Also, the Canon camera is basically dif-

ferent from the other cameras due to the fact that it is a color

camera and it is not very common for this type of camera to be

used for DIC or PIV applications.

Besides the experiments performed using the different cam-

era/lens combinations, two additional experiments were per-

formed using the Genie/Zeiss combination, but under different

imaging conditions. One of the two additional experiments was

performed while the lens was slightly defocused to produce

slightly blurred images, whereas in the other one, the camera

gain was set to a high value of 11 dB (the default setting of the

camera is zero gain). In the experiment with high gain setting,

the intensity of illumination was reduced to compensate for the

increased gain such that the average image intensity level was

comparable to the other experiments.

In the experiments conducted in this study, close attention

was paid to ensure that the same experimental conditions, set-

tings, and procedures were used for all experiments in order to

obtain a one-to-one comparison between the different cameras/

lenses that were investigated. A picture of the experimental

setup is shown in Fig. 1. In each of the experiments, the camera

was mounted on a multi-axis translating/rotating stage to allow

adjusting the position of the camera with respect to the target

and the same multi-axis stage was used for performing the

rigid-body-translation experiments. To avoid any confusion, it

might be worth mentioning here that the camera was translated

during the experiments rather than translating the target and

that basically gives the exact same outcome (that was done sim-

ply because the same setup was also used for other experiments

that are out of the scope of this paper). A printed random

speckle pattern having black dots on a white background was

attached to a flat plate. The average diameter for the dots of the

speckle pattern was about 0.5mm and the average dot center-

to-center spacing was about 1.2mm. The target was illuminated

using an adjustable intensity illumination source coupled with a

fiber-optic delivery cable. The distance between the front end of

the lens and the target surface (i.e., the working distance) was

set to be between 750 and 800mm according to camera/lens

combination being used. The camera-target working distance or

the zoom level (for zoom lenses) was adjusted such that the

field-of-view observed by the camera is 100mm wide for all

camera/lens combination that were used. Since the field-of-view

width was fixed for all experiments, the image scale-factor for

TABLE 2 The main specifications of the different lenses used in the experiments.

Lens ZeissMakro-Planar - ZF Pentax C5028-M Nikon Series-E Zoom Lens Canon EF-S Zoom Lens

Focal length 50mm 50mm 75 – 150mm 18 – 55mm

Aperture f/2 - 22 f/2.8 -22 f/3.5 - 32 f/3.5 - 5.6

Mount F-mount C-mount F-mount EF-mount

TABLE 3 The different camera/lens combinations used in the experiments along with the abbreviations used for identifying each of the cameras and

lenses.

Camera SensiCam (SC) Genie (Gn) Photon Focus (PhF) Canon (Cn)Lens

Zeiss (Zs) � � �Pentax (Pn) �Nikon zoom (Nk-z) �Canon zoom (Cn-z) �

HIJAZI AND KAHLER ON IMAGING SYSTEM EFFECT ON 2D-DIC ERROR 5

the different cameras varied according to the camera resolution.

The scale-factors for the different cameras used here were: 13.8

pixels/mm for SensiCam, 13.6 pixels/mm for Genie, 13.1 pixels/

mm for Photon-Focus, and 42.7 pixels/mm for Canon. Also, for

all camera/lens combinations, the camera position was initially

adjusted to capture the exact same region of the speckle pattern.

In each of the experiments conducted using the different

camera/lens combinations, great care was taken to ensure the

perpendicularity of the camera with respect to the target surface

to prevent any measureable errors that might be caused by cam-

era non-perpendicularity from hindering the results of this

study. An electronic level with laser pointer was used for orient-

ing the cameras perpendicular to the target surface. The camera

perpendicularity was then verified using rigid-body-translation

experiments based on the procedure presented in Ref. [18]

where the perpendicularity error (if any is present) was deter-

mined to be less than 0.5�. Also, care was taken to obtain similar

image brightness levels (an average image brightness of about

150 on 8-bit grayscale) regardless of the camera/lens combina-

tion being used, except for the Canon camera, which was run in

its “Auto” mode. The image brightness was controlled by

adjusting illumination intensity while the aperture of the lenses

was set at an intermediate value (around f/11). Furthermore, all

the cameras that were used in this study were allowed to run for

1 h, in order to let the FPA temperature to reach steady state

(such that the image noise level is stabilized), before starting

to capture images for the experiments. This is particularly

important for the SensiCam camera since it has a cooled FPA.

It should also be noted here that some of the cameras used

here have dynamic ranges higher than 8-bit, as can be seen

from Table 1. However, in order to eliminate any effect that the

dynamic range might have on the results, all the images used

for the experiments were recorded at 8-bit. For the color images

captured by the Canon camera, image processing software was

used for converting the images into 8-bit grayscale images.

The exact same rigid-body-translation experiment was

repeated for all camera/lens combinations. Starting from the

initial position, the camera was translated in two steps along the

x-direction, then in two steps along the y-direction and two

duplicate images were captured at each position. Each of the

two translation steps, in both the x and y directions, was equal

to 8 mm (8 % of the field-of-view width). As a result, images

were captured while the camera was at five different positions; a

reference position (i.e., the position after the first two transla-

tion steps in the x-direction), two translation steps in the

x-direction, and two translation steps in the y-direction. Fig. 2

illustrates the positions of series of images captured during the

experiments relative to the fixed target. The rectangular frames

shown in the figure represent the boundaries of the image in

each of the five different positions, where the solid line identifies

the reference position and the dashed and dotted lines identify

the two translated positions along the x and y directions. The

figure also shows the square region of interest used for DIC

analyses (identified using dashed line).

FIG. 1

The experimental setup.

Journal of Testing and Evaluation6

Analyses

DIC ANALYSES

The analyses were performed using a 2D-DIC software called

MatchID-2D [29]. In order to use the exact same region of the

image in all DIC analyses, a square region of interest corre-

sponding to a size of about 59� 59mm of the speckle pattern

was located in the upper central region in the reference image,

as illustrated in Fig. 2. However, the size of this region of inter-

est in pixels was different according to the resolution of the

camera being used. Also, since the cameras have different reso-

lutions, different DIC parameters in terms of subset size and

step size were used in order to have a direct one-to-one compar-

ison between the different cameras. Table 4 lists the size of the

region of interest, subset size, and step size (in pixels) used for

DIC analyses for the images captured by each of the four differ-

ent cameras. From the table, it can be seen that the step was

taken to be about half of the subset size in all cases in order to

get 50 % overlap between adjacent subsets. It also should be

noticed that though different values are used for the different

cameras (as seen in the table), they actually correspond to about

the same physical size on the speckle pattern (59� 59mm

region of interest, 2.25� 2.25mm subset size, and 1.1mm step

size) since the image scale-factors are different. The Normalized

Cross-Correlation algorithm was used for the DIC analyses of

all the different experiments and no image pre-filtering was per-

formed on the images. After obtaining the displacement maps

in both x and y directions (i.e., u and v), the Green-Lagrange

strains were calculated using a strain window size of 7� 7

points for all cases (that corresponds to a physical size of about

6.6� 6.6mm for the strain window). No further smoothing was

performed on the obtained strain maps.

As mentioned earlier, two duplicate images were recorded

by the camera while it was at each of the different positions dur-

ing the rigid-body translation experiments. These duplicated

images were correlated with each other where one of the images

was taken as the reference image, while the other was taken as

the deformed image. Since the two images were captured at the

same position, the correlation should give zero displacement at

all points in the x and y directions. However, due to the noise in

the digital images which cause some random fluctuation in the

image intensity values, the DIC results show very small random

sub-pixel displacements at all points. The displacements

obtained from such correlation represent the baseline error in

DIC analysis. Also, such correlation is useful in verifying

whether the correlation parameters being used are appropriate

or not. For each camera/lens combination, the correlations were

performed between each of the five pairs of duplicated images,

FIG. 2

The positions of the series of images captured

during the experiments.

TABLE 4 The DIC size parameters for the different cameras used in the experiments.

Camera SensiCam Genie Photon Focus Canon

Region of interest (pixel) 800� 800 800� 800 780� 780 2520� 2520

Subset size (pixel) 31� 31 31� 31 29� 29 97� 97

Step size (pixel) 15 15 14 48

HIJAZI AND KAHLER ON IMAGING SYSTEM EFFECT ON 2D-DIC ERROR 7

which correspond to the five different positions during the

rigid-body translation experiment, and the results of the five

correlations were averaged to get a more reliable estimate of the

baseline error.

For each group of rigid-body-translation experiments

corresponding to a different camera/lens combination, the ref-

erence position image was correlated with the images corre-

sponding to each of the two translation steps in each of the two

directions. Since two duplicated images were captured at each

position, a total of four duplicated correlations were performed

for each translation step (e.g., position 1-1 & position 2-1, posi-

tion 1-1 & position 2-2, position 1-2 & position 2-1, and

position1-2 & position 2-2). The results of the four replicates

were averaged in order to eliminate any variation in the results

that might be caused by the instability of the image intensity

values (though such differences were found to be very small).

ERROR ANALYSES

As mentioned earlier, the measurement accuracy of 2D-DIC

depends on several factors, and numerous studies have investi-

gated the influence of the different sources of error on the accu-

racy of the results. However, there is still a lack of a common or

standard procedure for evaluating the accuracy of DIC meas-

urements. Patterson et al. [30] proposed and presented standar-

dized test material and procedure for the evaluation of optical

techniques and systems used for full-field strain measurements.

They demonstrated the use of their proposed approach for DIC

and electronic speckle pattern interferometry (ESPI); however,

that approach is still not widely accepted among DIC users.

Hoult et al. [31] compared DIC strain measurements to the

strains measured using strain gauges during tensile testing.

They averaged the DIC strain values within a region of interest

and simply compared the averaged strain value to the strain

measured using strain gages to evaluate the accuracy of DIC

strain measurements. However, this simple approach does not

evaluate the accuracy of DIC strain maps since it is based on an

averaged value for DIC strain.

In general, the vast majority of studies related to DIC accu-

racy or error analysis can be grouped into two broad categories

according to their procedure. In the first category, synthetic

images are used where an image of a speckle pattern is numeri-

cally modified. A known amount of translation, rotation, homo-

geneous or heterogeneous deformation, is applied to the image;

then this new modified image is correlated to the reference (i.e.,

initial) image to determine the deformation. The results are

then compared to the applied translations or deformations in

order to assess their accuracy [11]. These types of studied are

useful for assessing the relative accuracy of the different correla-

tion algorithms as well as evaluating the effect of different

parameters (e.g., correlation parameters, speckle pattern, image

intensity, image contrast, etc.) on the accuracy of the results.

However, the effect of the imaging system and its optical

components on DIC accuracy is not accounted for in the error

estimates obtained by such studies. The use of such synthetic

images is very common for evaluating the accuracy of the differ-

ent correlation algorithms in PIV analyses [10].

The second category of studies basically uses in-plane rigid-

body-translation (or rotation) experiments to investigate the

accuracy of DIC measurements [15–18,21–24]. In rigid-body-

translation experiments, the target surface can be translated

with a known magnitude and direction, but, most importantly,

all points on the surface are translated by the same amount;

thus, the strains are zero. The accuracy of DIC measurements

can be assessed based on the displacement or strain results.

When the error assessment is based on displacement, usually,

the standard deviation of the obtained displacement values of

all points within the region of interest is calculated. Theoreti-

cally, all points have the same displacement during rigid-body-

translation and thus the standard deviation should be zero.

Therefore, the value of the displacement standard deviation,

usually reported in pixel units, is considered to represent the

magnitude of error in the displacement measurements. This

kind of displacement error estimation is usually used in PIV

analyses [12,13]. On the other hand, when the error assessment

is based on strains, any strains obtained from the DIC analysis

reflect an error in the results since the strain should in fact be

zero. The “mean” strain value (ð1=NÞP

e) for all points within

the region of interest can be calculated; however, this value will

be meaningful only when the strains obtained at all points are

positive or negative. This will be the case if the camera was not

perpendicular to the surface or if an out-of-plane displacement

occurred during the experiment [18]. Instead, the mean of the

strain absolute values (ð1=NÞP

ej j) is calculated where it can be

considered as a measure of the magnitude of error in DIC strain

measurements [16,18]. In addition, the standard deviation of

the strain values� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

e� �eð Þ2=Nq �

is also considered by many

researchers as a measure of the magnitude of error in DIC strain

measurements [11]. Some other researchers report the maxi-

mum strain value as a representation of the magnitude of strain

error [22]; however, such an approach is rarely used since it

exaggerates the magnitude of error.

Results and Discussion

THE DIFFERENT DIC ERROR ESTIMATION PARAMETERS

As mentioned in the previous section, the accuracy of DIC

analyses can be assessed based on the displacements or strains

obtained during rigid-body translation experiments. Three dif-

ferent parameters are commonly used for estimating the magni-

tude of error in DIC analyses and these parameters are: (1) the

standard deviation of the obtained displacements, (2) the mean

of the absolute values of the obtained strains, and (3) the stand-

ard deviation of the obtained strains. The standard deviation of

Journal of Testing and Evaluation8

the obtained displacement field is commonly used for reporting

the accuracy in PIV analyses since no subsequent strain calcula-

tions are done. The accuracy (or magnitude of error) in such a

case is usually given in pixel units, or it can be converted to dis-

placement units (mm or so) knowing the scale-factor of the

digital images. For DIC analyses, it is more common to report

the accuracy as the magnitude of error in the strain measure-

ments (the mean of absolute values or the standard deviation).

The three different error estimation parameters were calculated

for all the experiments performed in this study. Fig. 3 shows a

comparison of the three different DIC error estimation parame-

ters for one of the camera/lens combinations (SC/Zs) during

rigid-body-translation along the x-axis. As can be seen in the

figure, the three different error estimation parameters show a

somewhat similar increasing trend as the magnitude of the

rigid-body translation increases. This trend of increasing error

as the magnitude of displacement increases can be seen in all

the different experiments performed in this study and it is also

consistent with the results reported in literature [5,11,15,16,18].

Comparing the mean of absolute values and the standard devia-

tion of the obtained strains, it can be seen that the standard

deviation has a consistently higher magnitude. This difference is

quite understandable knowing that the errors are randomly dis-

tributed, and they usually follow a normal distribution [18,22].

Thus, the standard deviation value is bigger than about 68 % of

the data points, whereas the mean of absolute values is practi-

cally bigger than about 50 % of the data points. Thus, since the

standard deviation gives a more conservative estimate of the

strain error (since it has a higher value), it will be used for rep-

resenting the magnitude of DIC strain measurement error for

comparing the different camera/lens combinations.

Furthermore, it can also be seen from Fig. 3 that the dis-

placement error increases at a much faster rate compared to the

strain error, as the magnitude of translation increases. By

inspecting the values in the figure, it can be seen that the error

in the measured displacements increases from about 0.005 pixel

when the magnitude of translation is zero to about 0.039 and

0.076 pixels for 8 and 16mm of rigid-body-translation, respec-

tively. This observation calls for caution when dealing with PIV

or DIC displacement error values reported in literature where

any value must be associated with its corresponding magnitude

of translation. The fast increasing trend of the displacement

error, as compared to the strain error, can be attributed to the

fact that the strain is calculated using a relatively large strain

window (7� 7 points strain window size was used in this study,

whereas the smallest possible window size setting is 3� 3

points). As the strain calculation window size gets larger, more

displacement data points are used for calculating each strain

data point, and this results in smoothing out the random error

in the measured displacements and thus the magnitude of the

measured strain error is reduced. However, the use of large

strain windows is common in DIC analyses where some

researchers report using a strain window as large as 21� 21

points [21]. In general, the use of large strain window sizes

reduces the strain error, but at the same time, it reduces the

effective spatial resolution of the strain map and thus can

hinder any high strain gradients that might be present. Pan

et al. [5] recommend using large strain calculation windows for

measuring homogeneous deformation. On the other hand, for

inhomogeneous deformation, they generally recommend

smaller strain calculation windows such that a balance can be

obtained between accuracy and smoothing.

Fig. 4 provides another insight regarding PIV or DIC

displacement error. The figure shows a comparison of the dis-

placement errors (in pixels) for four different camera/lens com-

binations. It can be seen in the figure that the displacement

error for the Canon camera is much higher than it is for all the

FIG. 3 Comparison of the three DIC error estimation parameters (mean of

absolute strain values, strain standard deviation, and displacement

standard deviation) for rigid-body translation along x-axis (SC/Zs).

FIG. 4 Comparison of the DIC displacement error for four different camera/

lens combinations.

HIJAZI AND KAHLER ON IMAGING SYSTEM EFFECT ON 2D-DIC ERROR 9

other cameras. In fact, there are reasons for the higher DIC

measurements error associated with the Canon camera, as will

be discussed in a later section. However, the large difference

seen in Fig. 4 is mainly attributed to the fact that this camera

has a much higher image scale-factor than the other cameras

(due to its much higher digital resolution). For instance, for

16mm displacement, the displacement error for the Photon-

Focus camera is 0.18 pixels, while for the Canon camera, the

error goes to 1.18 pixels (about six folds the magnitude). How-

ever, since the scale-factor for the two cameras is quite different

(13.1 pixels/mm for Photon-Focus, and 42.7 pixels/mm for

Canon), if we convert these displacement error values and rep-

resent them in millimeters, the difference goes down and the

displacement error for the Photon-Focus becomes 0.013mm,

whereas for the Canon it becomes 0.028mm (about two folds

the magnitude, only). This observation brings to attention that

reporting the displacement error in pixel units can be mislead-

ing if it is not associated with the scale-factor of the digital

images. In fact, reporting the displacement error in pixels as an

independent measure of accuracy (i.e., without reporting the

associated scale-factor) can lead to a false impression that

higher measurement accuracy can simply be attained by using

higher resolution cameras.

CAMERA EFFECT ON DIC STRAIN ERROR

A comparison showing the effect of the camera on DIC strain

measurement error is presented in Fig. 5. The figure shows the

strain error (standard deviation) for four different cameras. For

the first three cameras (SensiCam, Genie, and Photon-Focus),

the same lens was used in the experiments such that a direct

one-to-one comparison can be made between the cameras.

However, the fourth camera (Canon) was used with the zoom

lens supplied with it since the other lenses do not fit this cam-

era. Moreover, it should be noted that the Canon camera used

here is a regular photography digital-SLR color camera and it is

not intended to be used for scientific applications. Nevertheless,

some DIC software companies commercialize similar cameras

as an alternative for field measurements. Also, some researchers

report using similar SLR digital cameras in DIC measurements

[16,31,32]. Thus, the Canon camera was used in this study in

order to compare its performance in DIC measurements with

other cameras that are typically used in DIC or PIV applica-

tions. As can be seen in the figure, for all of the four cameras,

the magnitude of strain error increases as the magnitude of dis-

placement increases. For the Canon camera, though the strain

error at zero displacement is relatively small, it increases at a

faster rate as the displacement increases. The high magnitude of

strain error for the Canon camera relative to the other cameras

is most likely due to two reasons. Firstly, and most importantly,

comes the fact that this is a color camera; secondly, that a zoom

lens is used with this camera. Color cameras are equipped with

imaging sensors that are covered with a mosaic pattern of red,

green, and blue filters. As the target translates, points on the tar-

get that were initially imaged through one of the color filters get

imaged through a different color filter and so on, causing varia-

tion in the image intensity at the pixel level between successive

images. Regarding the zoom lens used with the Canon camera

in general, it is well known that zoom lenses produce lower

quality images than fixed focal length lenses. This is because

optical aberrations cannot be effectively corrected at the entire

focal length range of the zoom lens. However, it will be seen

from the next section that the use of zoom lens will not result in

very significant increase in error such as that seen with the

Canon camera. In summary, though the Canon camera digital

resolution is much higher than the other cameras used in this

study, the fact that it has a color sensor and the zoom lens used

with it, evade any benefit of the height digital resolution, if any.

In fact, Reu et al. [23] report that there is no benefit for using

high resolution cameras in DIC measurements if the lens reso-

lution is lower than that of the camera.

As mentioned earlier, the magnitude of strain error at zero

displacement represents the baseline error value for any cam-

era/lens combination. The figure shows that strain error, at zero

translation, is lower for the Photon-Focus and Canon cameras

than that of the other two cameras. This difference can be

attributed to the fact that the Photon-Focus and Canon cameras

have CMOS sensor, whereas the other two cameras have CCD

sensor. As mentioned previously, the CMOS sensors represent

the latest technology in imaging sensors and, in general, they

provide better stability in terms of the image intensity levels as

compared to CCD sensors. A study done by Hain et al. [28],

which compared CCD and CMOS sensors, showed that CMOS

sensors have better signal-to-noise ratio (SNR) than CCD sen-

sors. Thus, this lower strain error level at zero displacement is

simply due to the higher stability in image intensity levels

resulting from the height SNR of the CMOS sensors.

FIG. 5 Comparison of the camera effect on DIC strain error.

Journal of Testing and Evaluation10

Comparing the strain errors for the SensiCam and Genie

cameras, it can be seen that almost no difference can be seen

between the results of the two cameras. These results suggest

that the relatively low cost industrial machine vision cameras

may perform as good as the more expensive specialized scien-

tific cameras such as the SensiCam (however, it should be kept

in mind that the SensiCam is capable of capturing image pairs

with a inter-frame time of a few microseconds, which is a capa-

bility not available in the industrial machine vision cameras).

Also, it can be seen from the figure that though the strain error

for the Photon-Focus camera is clearly lower than that of the

SensiCam and Genie at zero displacement, it increases and

becomes slightly higher than that of the two cameras when the

target is translated. As discussed previously, the low strain error

at zero displacement is due to the stability of the image intensity

levels for the CMOS sensors. However, CMOS sensors are

known to have lower fill factor compared to CCD sensors due

to the presence of the digitization circuitry for each pixel on the

sensor itself [26]. Thus, when translation occurs, the low fill fac-

tor of the CMOS sensor comes into effect and, apparently, it

evades the advantage of the higher stability of the image inten-

sity levels.

Finally, the results presented in Fig. 5 show that the level of

the strain error obtained with three of the cameras tested here is

about 0.0003 (i.e., 300 micro-strains) for 8mm displacement

(which represents 8 % of the field of view width, as mentioned

earlier). This level of strain error seems to be very low when

compared to plastic strains in ductile materials. However, tradi-

tional strain measuring devices, such as strain gauges for

instance, still provide strain measurements with higher accuracy

than DIC. A comparison done by Patterson et al. [30] showed

that electronic speckle pattern interferometry (ESPI) and strain

gauges give higher accuracy than DIC for the measurement of

elastic strains. Hild and Roux [33] demonstrated that DIC can

be employed for the identification of elastic properties of low

stiffness materials using a Brazilian disk made of polycarbonate

polymer. In general, the DIC method is a powerful and widely

accepted method for measuring strains in the plastic range of

deformation (or in the elastic range for low stiffness materials

such as polymers) where the strains are relatively large, but, it

found very limited success for measuring small strains such as

the elastic strains in stiff materials (e.g., metals and ceramics).

For instance, if we take carbon steel as an example, the maxi-

mum elastic strain for most carbon steels is in the range

0.002–0.004. The results presented here imply that though the

magnitude of the DIC strain error is relatively small (about 300

micro-strains), but still it is not considered that small when

compared to the values of elastic strains of stiff materials (such

as carbon steel for example). Based on that, it is reasonable to

believe that DIC method is not a good choice for accurately

measuring elastic strains in stiff materials, especially when high

strain gradients are present. It might be worth mentioning here

that though smaller strain error estimates might sometimes be

found in literature, that does not necessarily reflect higher accu-

racy. It should be kept in mind that it is possible to further

reduce the estimated strain error by using larger strain window

size (a 7� 7 points strain window was used in this study, as

mentioned earlier) and/or employing a filter to smooth the

strain map. However, doing such will result in reducing the

effective resolution of the 2D strain map.

The results presented here for comparing the different cam-

eras shows that the rigid-body-translation experiments and the

approach followed in this paper can be used as a simple and

direct method for evaluating and comparing the metrological

performance of cameras and in particular their suitability for

use in full-field deformation measurement [28,34].

LENS EFFECT ON DIC STRAIN ERROR

Fig. 6 shows a comparison of the DIC strain error values

obtained using three different lenses (Zeiss, Pentax, and Nikon

zoom) with the same camera (Genie). From the figure it can be

clearly seen that there is an appreciable difference between the

strain error values obtained using the three different lenses. In

fact, the difference in strain errors seen here is more pro-

nounced than that seen previously in Fig. 5 (except for the

Canon camera), which indicates that the effect of the lens on

DIC strain measurement accuracy can be more significant than

the effect of the camera. The figure shows that the Zeiss lens

gives the highest accuracy rather than the Pentax lens then the

Nikon zoom lens. This trend is actually not surprising where it

is consistent with the known quality of these lenses (it is even

consistent with the price tags of these lenses). As in the previous

figures, the usual trend of increasing strain error as the displace-

ment increases can also be in this figure. The reason behind the

difference in the magnitude of strain measurement error

obtained using the different lenses can simply be attributed to

the presence and severity of optical aberrations in these lenses.

FIG. 6 Comparison of the lens effect on DIC strain error.

HIJAZI AND KAHLER ON IMAGING SYSTEM EFFECT ON 2D-DIC ERROR 11

Different types of optical aberrations such as field curvature,

coma, distortion, astigmatism, spherical, etc., can be present in

lenses [35]. Lens manufacturers design their lenses in order to

correct these aberrations, but the effectiveness and accuracy of

these corrections vary between the different types of lenses.

Fig. 7(a) and 7(b) show the DIC horizontal displacement “U”

maps obtained from the images captured using the Zeiss and

Pentax lenses at zero, 8, and 16mm rigid-body-translations.

From the figure, it can be seen that the “U” displacement error

looks random at zero translation, while there is a clear and dis-

tinct displacement error pattern associated with each of the two

lenses that can be seen at both 8 and 16mm translations. The

displacement error patterns seen in the figure reflect the optical

distortion in the images formed by each of the two lenses. How-

ever, at zero translation, the lens distortion cannot be captured

by DIC analysis since the image is correlated with a reference

image captured while the camera is imaging the same position

(two duplicate images). But nevertheless, by referring again to

Fig. 6, it can be seen that the effect of the lens on DIC strain

error is also present at zero translation, which is a bit surprising

but still explainable. The lens effect on DIC strain error seen at

zero translation is basically related to the difference in definition

(i.e., sharpness) of the optical images formed by the different

lenses. Such difference cannot be recognized by the naked eye

in many cases; however, its effect is captured by the DIC analy-

sis. Higher definition images of the black and white speckle

pattern will show steeper change in the intensity levels of the

digital images between the black and white regions. This steep

change in intensity levels makes the matching of image subsets

more accurate and thus improves the displacement and strain

measurements accuracy.

By referring again to Fig. 7 and inspecting the shape of dis-

placement error patterns seen at 8 and 16mm translations for

each of the two lenses, it can be seen that the shapes of the error

patterns for the two lenses are quite different. The difference in

the error pattern shapes indicates that different types of optical

FIG. 7

DIC horizontal displacement “U” maps at Dx¼0, D x¼ 8 mm, D x¼ 16 mm, (a) Zeiss lens,

(b) Pentax lens.

Journal of Testing and Evaluation12

distortions are present in the two lenses. As mentioned earlier,

Pan et al. [21] and Lava et al. [22] proposed mathematical mod-

els and procedures for correcting for radial, radial and

tangential lens distortions, respectively. The shape of the error

pattern associated with the Zeiss lens looks somehow similar to

that caused by radial distortion [21]. However, the shape of the

error pattern associated with the Pentax lens looks a bit unusual

and cannot be entirely explained by radial and/or tangential

image distortions. This indicates that there is still a need for

more advanced models for correcting the different types of lens

optical distortions. In general, the results of this study are in

agreement with Refs. [21,22] in substantiating the call for carry-

ing out a calibration procedure in order to correct for the lens

distortions and thus reduce the magnitude of error in 2D-DIC

measurements.

IMAGE SHARPNESS AND CAMERA GAIN EFFECTS

ON DIC STRAIN ERROR

Fig. 8 shows a comparison of the DIC strain error values

obtained using one of the camera/lens combinations (Genie

camera with Zeiss lens) at three different imaging conditions. In

the first condition, which is the ordinary condition, the image

was well focused and the camera gain setting was set to its

default value of zero. In one of the other two conditions being

compared here, the image was slightly defocused (by changing

the focus setting of the lens), while in the other, the camera gain

was set to a high value. In the condition where the gain setting

was increased, the intensity of the illumination was reduced in

order to maintain the average image intensity level. As expected,

the results presented in the figure show that decreasing the

image sharpness reduces the DIC strain measurement accuracy.

Indeed, this observed relation between image sharpness and

strain error, confirms the conclusion drawn in the previous sec-

tion regarding the lens effect on strain error at zero translation.

The second comparison is made between the ordinary opera-

tional condition of the camera (zero gain setting) and when the

gain is set to a high value. Increasing the gain setting is an

option available in most digital cameras, and it is intended to

compensate for low illumination intensity. The figure shows

that increasing the gain increases the DIC strain error. The gain

effect seen here is rather expected since both the image intensity

levels and the random image noise are amplified when the gain

is increased.

DIRECTION OF TRANSLATION EFFECT ON DIC

STRAIN ERROR

As mentioned previously in the experimental procedure

section, the rigid-body-translation experiments performed in

this study involved translation steps in both the x- direction

and y-direction. In general, similar trends of increasing DIC

stain errors as the displacement increases can be seen for trans-

lations along the x-axis or the y-axis. Typically, researchers who

use rigid-body-translation experiments to study DIC strain

measurement accuracy perform the translations along one

direction. Moreover, all the results presented in the previous

figures are for translations along the x-axis, since it is of most

interest, because it is along the width of the image, which is

larger than the image height. In all the DIC analyses performed

in this study, the correlations were performed for a square

region of interest located at the top center of the image. By

using a square region of interest, the same number of data

points is present in both directions, and thus, the obtained

results will have the same statistical reliability in both directions.

Fig. 9 shows a comparison of the DIC strain errors, both �xx and

�yy , associated with translations along either the x-axis or the

y-axis (using the Genie camera and Zeiss lens). From the figure,

it can be seen that for zero translation, the error in both �xx and

�yy is comparable. It can also be seen that when the translation

FIG. 8 Comparison of the effects of image defocus and camera gain on DIC

strain error (Gn/Zs).

FIG. 9 Comparison of the �xx and �yy strain errors for translations in the

x-direction and y-direction (Gn/Zs).

HIJAZI AND KAHLER ON IMAGING SYSTEM EFFECT ON 2D-DIC ERROR 13

is in the x-direction, �xx becomes clearly larger than �yy (though

it also increases), and the opposite happens when the transla-

tion is in the y-direction. Since �xx is larger when the translation

is in the x-direction, it is taken as the component that reflects

the magnitude of strain error. Similarly, �yy is taken as the com-

ponent that reflects the magnitude of strain error when the

translation is along the y-direction. Furthermore, an interesting

observation can be made from Fig. 9 regarding the magnitudes

of strain errors associated with translations in the x and y direc-

tions. By inspecting the magnitudes of the strain errors, it can

be seen that strain errors resulting from translations in the

y-direction are clearly higher than those resulting from transla-

tions in the x-direction. To further investigate this observation,

a comparison was made between the DIC strain errors associ-

ated with translations along the x-axis and the y-axis for three

different cameras, and this comparison is shown in Fig. 10. It

can be seen from the figure that the magnitude of DIC strain error

is clearly dependent on the direction of the translation where the

error is clearly higher for all the three cameras when the transla-

tion is along the y-axis. One might simply think that this differ-

ence is due to a problem in the alignment of the camera with

respect to the target; however, the fact that the same trend is seen

with the three cameras, and knowing that each one of cameras

was setup independently and later verified, makes such idea to be

unrealistic. In fact, this directionality in DIC strain errors is most

likely due to the fill factor of the imaging sensor knowing that

interline-CCD and CMOS imaging sensors have different fill fac-

tors in the x and y directions. This observation indicates that the

alignment of the image with respect to the direction of translation

will influence the magnitude of error in DIC strain measure-

ments. The results shown in Fig. 10 suggest that, during any

experiment where DIC is used to measure the strains, better accu-

racy can be obtained by aligning the camera width direction with

the direction of the maximum displacement.

Concluding Remarks

Though there is no standard approach for estimating the

errors in DIC measurements, the use of in-plane rigid-body-

translation experiments is one of the most realistic and widely

accepted methods for estimating the errors in both the displace-

ment and strain measurements of 2D-DIC analysis. In this

study, rigid-body-translation experiments were used to investi-

gate the uncertainty of DIC displacement and strain measure-

ments associated with different types of imaging systems. Four

different cameras (with different resolutions and imaging sensor

types) and four different lenses (with different optical quality

and focal length) were used in this study. By doing the rigid-

body-translation experiments using different camera/lens com-

binations, the influences of both the cameras and lenses on DIC

measurements accuracy were identified, and the magnitude of

errors associated with these different types of cameras and

lenses was determined. The influence of different imaging con-

ditions such as out-of-focus effects (image un-sharpness) and

high camera gain were also investigated. Furthermore, the influ-

ence of the direction of translation on DIC measurements accu-

racy was identified. The results of this study provide a more

thorough understanding of the contribution of the imaging sys-

tem components in the overall DIC measurements error. It is

believed that the experimental approach used in this study can

be used for quantitatively assessing the accuracy and quality of

the different types of cameras and lenses and to determine their

suitability for use in experimental techniques such as DIC or

PIV. The main conclusions of this study can be summarized in

the following points.

• In-plane rigid-body-translation, experiments are usefulfor estimating the magnitude of baseline error in 2D-DICmeasurements. Such experiments, carried under closecontrol of the experimental conditions and correlationparameters, can be used for comparing different imagingsystems and for determining the contribution of theimaging system components in the measurement error.

• Three different parameters; namely, displacement stand-ard deviation, mean of strain absolute values, and strainstandard deviation, can be used as error estimationparameters in order to determine the accuracy of DICmeasurements. The displacement standard deviation issuitable for estimating the accuracy if strain measure-ments are not required (such as the case of PIV analysis).The strain standard deviation is more suitable than themean of strain absolute values for estimating the DICstrain error, since it is more conservative.

• Reporting the displacement error in pixel units as anindependent measure of accuracy (i.e., without the scale-factor) can be misleading where it gives a false impressionthat using cameras with higher resolution will automati-cally lead to higher measurement accuracy. For numericalerror estimation studies, the displacement error can

FIG. 10 Comparison of the DIC strain errors for translations in the

x-direction and y-direction using three different cameras.

Journal of Testing and Evaluation14

simply be reported in pixels. However, for physicalstudies (i.e., ones performed using actual images), thedisplacement error “in pixels” must be reported in con-junction with the image’s scale-factor, or alternatively,the error can be reported in displacement units (e.g., mmor lm) along with the image’s magnification level.

• The estimated strain measurement error is dependent onboth the correlation and strain calculation parameters,and thus all these parameters should be carefully chosenand controlled when comparing errors associated withdifferent imaging systems. Also, it should be noted thatthe estimated strain errors are directly influenced by thechoice and values of these parameters.

• All experiments show that the measurement errorincreases as the magnitude of translation increases. Thus,when reporting the magnitude of error, it should be asso-ciated with the corresponding magnitude of rigid-body-translation.

• For the cameras tested here, the results show that thetype of camera and imaging sensor do not have a signifi-cant effect on measurement accuracy, except for colorSLR cameras, which are not designed nor meant to beused for this type of applications.

• The type and quality of the lens has a clear effect on mea-surement accuracy, and it is generally more pronouncedthan effect of the camera itself.

• The lowest DIC strain error estimate for the camera/lenscombinations used in this study is about 300 micro-strains (at 8mm translation and 7� 7 points strainwindow size), which makes the applicability of DIC foraccurately measuring small elastic strains in stiff metalslike steel to be somehow questionable especially in thecase of non-homogeneous strain fields. A calibration pro-cedure to correct for lens optical distortions will be neces-sary to improve the measurement accuracy in such cases.

• There is a clear and significant effect for the direction oftranslation on measurement accuracy. For the camerastested here, the measurement error is significantly lowerwhen the translation is along the width direction of theimage.

ACKNOWLEDGMENTS

The first author is pleased to acknowledge the financial support

provided by the Hashemite University for his sabbatical leave.

He also acknowledges the financial support provided by the

German Research Foundation (DFG) for his research visit to

the Institute of Fluid Mechanics and Aerodynamics at Universi-

tat der Bundeswehr Munchen.

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